变转速工况下高速列车轴承转子系统特性分析

王宝森; 刘永强; 张斌

doi:10.6052/0459-1879-22-067

变转速工况下高速列车轴承转子系统特性分析

doi: 10.6052/0459-1879-22-067

王宝森^{*, †, **},
刘永强^*,,
张斌^**

*.
石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室, 石家庄 050043
†.
石家庄铁道大学交通运输学院，石家庄 050043
**.
南卡罗来纳大学工程与计算机学院, 美国哥伦比亚 29208

基金项目: 国家重点研发计划(2020YFB2007700), 国家自然科学基金(11790282, 12032017, 12002221, 11872256), 河北省科技计划(20310803D), 河北省自然科学基金(A2020210028), 河北省教育厅科技计划(ZD2021093)和留学基金委资助项目

详细信息

作者简介:
刘永强, 教授, 主要研究方向: 车辆系统动力学、预测和健康管理. E-mail: liuyq@stdu.edu.cn

中图分类号: U270.1⁺1
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出版历程
- 收稿日期: 2022-02-13
- 录用日期: 2022-04-25
- 网络出版日期: 2022-04-26
- 刊出日期: 2022-07-15

CHARACTERISTICS ANALYSIS ON BEARING ROTOR SYSTEM OF HIGH-SPEED TRAIN UNDER VARIABLE SPEED CONDITIONS

Wang Baosen^{*, †, **},
Liu Yongqiang^*
,,
Zhang Bin^**

*.
State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
†.
School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
**.
College of Computing and Engineering, University of South Carolina, Columbia 29208, South Carolina, USA

摘要

摘要: 高速列车的发展使得其关键零部件——轴承的安全问题日益突出. 现有的轴承模型均是建立在匀速工况下, 不能描述系统在变转速工况下运动状态. 为了解决这个问题, 建立了一个变转速工况下高速列车轴箱轴承转子系统动力学模型, 模型通过角度迭代计算得到了滚动体在不均匀时间内转过的总角度, 进而确定了滚动体在任意时刻的空间位置. 在匀速工况和变转速工况下, 对具有外圈故障的轴承模型进行了实验对比, 验证了模型的有效性. 利用轴心轨迹定性分析了外圈故障、内圈故障和滚动体故障对系统稳定性的影响, 并通过实验验证了分析结果的可靠性. 利用二维不变矩作为特征指标定量分析了三类故障对系统稳定性的影响. 分析结果表明: 当轴承角加速度较小时, 外圈故障对系统稳定性影响最大; 当轴承角加速度较大时, 滚动体故障对系统稳定性影响最大, 但是影响程度随着故障尺寸的变大而逐渐减小. 同样地, 利用二维不变矩作为特征指标进行了系统的稳定性临界状态分析, 确定了在不同转速工况下和不同故障类型下临界状态对应的最大故障尺寸. 研究结果表明: 随着轴承内圈转速的上升, 不同故障类型对应的最大尺寸都会减小, 其中滚动体故障尺寸大都是最小的, 说明滚动体故障对系统稳定性影响最大.
- 高速列车 /
- 轴承模型 /
- 变转速工况 /
- 稳定性分析 /
- 二维不变矩
Abstract: The development of high-speed trains has made the safety problem of its key components—bearings increasingly prominent. Existing bearing models are all established under uniform speed conditions and cannot describe the motion state of the system under variable speed conditions. To solve this problem, a dynamic model of the axle box bearing rotor system of a high-speed train under variable speed conditions is established. The model uses angle iteration to calculate the total angle that the rolling elements have rotated in an uneven time, and then determines the spatial position of the rolling elements at any time. Comparison experiments and simulations were carried out under constant speed and variable speed conditions, and they have a good agreement, which verifies the effectiveness of the model. The influence of outer ring fault, inner ring fault, and rolling element fault on the system stability are qualitatively analyzed by the axis trajectory, and the reliability of the analysis results is verified by experiments. The two-dimensional moment invariants are used as a characteristic indicator to quantitatively analyze the influence of three types of faults on system stability. The analysis results show that under uniform speed conditions, the effects of different types of faults on train stability are small. Under variable speed conditions, the outer ring fault has the greatest impact when the angular acceleration is slight, and the rolling element fault has the greatest impact when the angular acceleration is large, but the degree of impact gradually decreases with the size of the fault. Similarly, two-dimensional moment invariants are used to analyze the stability critical state of the rotor system and determine the maximum fault size corresponding to the critical state under different speed conditions and different fault types. The results show that that with the increase of the speed of the bearing inner ring, the maximum size corresponding to different fault types will decrease, and the fault size of the rolling element is mostly the smallest, indicating that the rolling element fault has the greatest impact on the stability of the system.
- high-speed train /
- bearing model /
- variable speed conditions /
- stability analysis /
- two-dimensional moment invariant

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图 1 轴承转子系统模型

Figure 1. Model of bearings and rotor coupling system

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图 2 轴承侧视图

Figure 2. Side view of the bearing

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图 3 轴承动力学模型

Figure 3. Bearing dynamics model

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图 4 轴承外圈、外圈故障和内圈故障示意图

Figure 4. The schematic diagram of the outer ring, the outer ring fault and the inner ring fault

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图 5 实验台和传感器安装位置示意图

Figure 5. The schematic diagram of the test rig and sensors’ location

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图 6 匀速工况下的仿真结果

Figure 6. Simulation results under constant speed condition

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图 7 匀速工况下的实验结果

Figure 7. Experimental results under constant speed condition

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图 8 变转速工况下的实验结果

Figure 8. Experimental results under variable speed condition

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9 变转速工况下的仿真结果

9. Simulation results under variable speed condition

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图 10 转子处轴心轨迹

Figure 10. Axis trajectory diagram at the rotor

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图 11 轴承处轴心轨迹

Figure 11. Axis trajectory diagram at the bearing

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图 12 外圈故障条件下对比结果

Figure 12. Results comparison under the condition of outer ring fault

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图 13 内圈故障条件下对比结果

Figure 13. Results comparison under the condition of inner ring fault

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图 14 轴承处轴心轨迹的φ₁和φ₂的值

Figure 14. Values of φ₁ and φ₂ of axis trajectory at bearing

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15 转子处轴心轨迹的φ₁和φ₂的值

15. Values of φ₁ and φ₂ of axis trajectory at rotor

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15 转子处轴心轨迹的φ₁和φ₂的值(续)

15. Values of φ₁ and φ₂ of axis trajectory at rotor (continued)

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图 16 三种角加速度下转子处轴心轨迹

Figure 16. Axis trajectory at rotor under the conditions of three angular accelerations

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图 17 不同转速条件下φ_1,ORF,rotor随故障尺寸的变化规律

Figure 17. Variation of φ_1,ORF,rotor with fault size at different rotating speeds

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表 1 轴承几何参数

Table 1. Geometric parameters of the bearing

Parameter	Value
mass of the inner ring m₁/kg	4.63
inner ring radius r/mm	65
total mass of the bearing m₂/kg	30
outer ring radius R/mm	120
numbers of roller N₀	17
average roller diameter d/mm	26.5
pitch diameter D/mm	156.25
load F/N	7.0205 × 10⁴

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表 2 轴承系统模型参数

Table 2. Parameter of the bearing system model

Parameter	Value
axle equivalent mass m_c/kg	274
stiffness of axle C/(N·s·m⁻¹)	2 × 10³
damping of axle K/(N·m⁻¹)	1.48 × 10⁷
mass eccentricity of axle section e/mm	10^-5
stiffness of inner ring C₁/(N·s·m⁻¹)	7 × 10⁴
damping of inner ring K₁/(N·m⁻¹)	3.05 × 10⁸
stiffness of outer ring C₂/(N·s·m⁻¹)	7 × 10⁴
damping of outer ring K₂/(N·m⁻¹)	2 × 10¹⁰
contact damping K_t/(N·m⁻¹)	3.5 × 10¹⁰

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表 3 单元谐振器参数

Table 3. The parameter of the unit resonator

Parameter	Value
mass m_b/kg	1
damping K_b/(N·m⁻¹)	8.8826 × 10⁹
stiffness C_b/(N·s·m⁻¹)	9.424 × 10³

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表 4 不同转速条件下稳定性临界状态对应的最大故障尺寸

Table 4. Maximum fault size corresponding to stability critical state under different speed conditions

Fault types	Bearing angular speed/(r·min⁻¹)
Fault types	100	600	1100	1600	2100
inner ring fault	0.99	0.76	0.65	0.91	0.53
roller fault	0.42	0.78	1.03	0.68	0.23

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